Question

Tell whether the lines of the pair of equations are parallel, perpendicular, or neither.

Answer 1

First Equation:

$y= -\frac{3}{4} x+2$

Second Equation can be written as:

$y= \frac{3}{4}x+2$

Slope of first equation is -3/4 and slope of second equation is 3/4. 
Slope of parallel lines must be equal, and slope of perpendicular lines are the negative reciprocal of each other. None of these conditions can be seen for given two equations.

So, the two lines are neither parallel nor perpendicular.
So correct option is C

Answer 2

Answer:
neither

Explanation:
Before we begin, note the following:
For two lines to be parallel, their slopes have to be equal
For two lines to be perpendicular, the product of their slopes has to be -1

Now, for the given:
The general form of the linear equation is:
y = mx + c where m is the slope and c is the y-intercept

For the first given equation:
y = -3/4 x + 2
By comparing with the standard form, we can note that:
slope = -3/4

For the second given equation:
3x - 4y = -8
Putting it in the standard form:
4y = 3x + 8
y = 3/4 x + 2
By comparing with the standard form, we can note that:
slope = 3/4

Now, let's check:
we have:
m1 = -3/4
m2 = 3/2

m1 is not equal to m2 .......> lines are not parallel
m1 * m2 = -3/4 * 3/4 = -9/16 which is not equal to -1 .....> lines are not perpendicular

The graph of the two lines is shown in the attached image

Hope this helps :)